Flavor structure and coupling selection rule from intersecting<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>-branes

Abstract

We study flavor structure and the coupling selection rule in intersecting $D$-brane configurations on ${T}^{2}\ifmmode\times\else\texttimes\fi{}{T}^{2}\ifmmode\times\else\texttimes\fi{}{T}^{2}$ as well as its orbifold/orientifold compactifications. We formulate the selection rule for Yukawa couplings and its extensions to generic $n$-point couplings. We investigate the possible flavor structure, which can appear from intersecting $D$-brane configuration. Then, we show there is a certain rule among intersecting numbers for states corresponding to allowed Yukawa couplings, and also it is found that their couplings are determined by discrete Abelian symmetries. Our studies on the flavor structure and the coupling selection rule in this class of models show that there is no solution to derive realistic Yukawa matrices only from stringy 3-point couplings at the tree-level within the framework of the minimal matter content of the supersymmetric standard model.